A ( $$3+1$$ )-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton solutions are constructed. In the process of degeneration solutions, T-breathers derived by taking complexication method. Then rogue will emerge during breathers parameter limit Through full N-soliton, M-lump based long-wave...

In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation. Keywords—Exact solution, The (3+1)-dimensiona...

Exact solutions of higher-dimensional nonlinear equations takes a major place in the study phenomena observed nature. In this article, some new kink type are investigated for (3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. Firstly, variety obtained by Hirota’s bilinear form, which include wave solution, periodic solitary and singular using extended homoclinic test approach. Second...